Active acoustic control in quiet gradient coil design for MRI

ABSTRACT

Acoustically controlled magnetic coils comprise first and second electrical conductors which are mechanically coupled by a block of material of defined acoustic transmission characteristics which holds the conductors a predetermined distance apart. The conductors are supplied with currents of different and variable amplitudes and different and variable relative phases both of the features being determined by the acoustic characteristics and by the geometry and predetermined distance.

The present invention relates to acoustically quiet gradient coil designin magnetic resonance imaging (MRI).

Magnetic gradient coils are a prerequisite for NMR imaging (P. MansfieldP. and P. G. Morris, NMR Imaging in Biomedicine. Academic Press, N.Y.(1982)) and also for use in a range of NMR applications includingdiffusion studies and flow. In NMR imaging the acoustic noise associatedwith rapid gradient switching combined with higher static magnetic fieldstrengths is at best an irritant and at worst could be damaging to thepatient. Some degree of protection can be given to adults and childrenby using ear defenders. However, for foetal scanning and in veterinaryapplications, acoustic protection is difficult if not impossible.

Several attempts have been made to ameliorate the acoustic noiseproblem. For example, by lightly mounting coils on rubber cushions, byincreasing the mass of the total gradient assembly and by absorptivetechniques in which acoustic absorbing foam is used to deaden the sound.Acoustic noise cancellation techniques have also been proposed whichrely on injection of antiphase noise in headphones to produce alocalised null zone. These methods are frequency and position dependentand could possibly lead to accidents where, rather than cancel thenoise, the noise amplitude is doubled.

The present invention relates to a novel method for active control ofacoustic output in quiet magnetic gradient coil design henceforthreferred to simply as active acoustic control in magnetic coils andmagnetic gradient coils which readdresses the cause of the acousticnoise problem over that achieved in uncontrolled active acousticshielding (P. Mansfield, B. Chapman, P. Glover and R. Bowtell,International Patent Application, No. PCT/GB94/01187; Priority Data9311321.5, Jun. 2, (1993); P. Mansfield, P. Glover and R. Bowtell,Active acoustic screening: design principles for quiet gradient coils inMRI. Meas. Sci. Technol. 5, 1021-1025 (1994); P. Mansfield, B. L. W.Chapman, R. Bowtell, P. Glover, R. Coxon and P. R. Harvey, Activeacoustic screening: Reduction of noise in gradient coils by Lorentzforce balancing. Magn. Reson. Med. 33, 276-281 (1995)) and offersconsiderable improvement in noise suppression.

The present invention provides an active acoustically controlledmagnetic coil system which is adapted to be placed in a static magneticfield, the coil comprising a plurality of first electrical conductorsand a plurality of at least second electrical conductors, the first andat least the second conductors being mechanically coupled by means of atleast one block of material with a predetermined acoustic transmissioncharacteristic and in which the first and at least the second conductorsare spaced at a predetermined distance apart, first electrical currentsupply means for supplying a first alternating current to said firstelectrical conductor, at least a second electrical current supply meansfor supplying at least a second alternating current to said at leastsecond electrical conductor, said first and at least second currentscharacterised in that they have different and variable amplitudes anddifferent and variable relative phases, both these features beingdetermined by the acoustic characteristics of the material and by itsgeometry and the predetermined distance.

The first and second current supply means may comprise means forsupplying current waveforms with controllable shape said waveforms beingshaped to fit the wave propagation properties characteristics of themechanical coupling material. The currents can be rectangular ortrapezoidal waveforms and in these cases the second current waveformwill be delayed with r respect to the first. The phrase "alternating" istherefore extended to include rectangular or trapezoidal waveforms andthe phrase "variable relative phases" is extended to include a delayedsecond waveform.

The leading and trailing edges of the second waveform will be delayed intime and accordingly shaped to fit the wave propagation propertiescharacteristic of the mechanical coupling material by matching thewaveform to that arriving on the far side of the material block throughwhich the acoustic wave is travelling.

Preferably the amplitude of the second current is calculated to be adefined ratio of the amplitude of the first current, the defined ratiobeing a function of both the distance by which the first and secondconductors are separated and the acoustic transmission characteristicsof the coupling material.

In a preferred embodiment the first electrical conductor forms an outerloop and the second electrical conductor forms an inner re-entrant loop.

Preferably the inner re-entrant loop comprises first and secondsubstantially parallel path portions connected by a relatively shortjoining portion, the first and second portions being embedded in firstand second separate material blocks, the blocks being mechanicallycoupled together.

Preferably the coupling can comprise an air gap with spacers positionedat intervals to separate the first and second blocks.

Alternatively the mechanical coupling uses a suitable coupling material.

Preferably the coupling material is a polymer material or rubber whichmay be a different and softer material to that used to support the firstconductor or outer loop.

The present invention also provides a method of designing an activeacoustically controlled magnetic coil system comprising the steps of:

a) defining first and second substantially parallel conductor paths;

b) defining an acoustic transmission material having predeterminedcharacteristics to encase the first and second parallel conductors at apredetermined distance apart;

c) determining a first alternating current at a first amplitude andphase to flow in the first parallel conductor path;

d) determining a second alternating current at a second amplitude andphase different to said first amplitude and phase to flow in the secondparallel conductor path,

the amplitude and relative phase of the second current being determinedby the acoustic characteristics of the material and by its geometry andthe predetermined distance.

In the present invention the substantially parallel paths may be arcuatefor example when the rectangular loops are deformed into closed arcloops. The term substantially parallel is in this invention defined asincluding equidistantly spaced arcuate paths.

The present invention also provides a coil structure comprising foursubstantially parallel conductors in a mechanically coupled systemincluding first and second outer conductors and first and second innerconductors, each first and second outer conductor being mechanicallycoupled to a respective first and second inner conductor by first andsecond blocks of material with defined acoustic transmissioncharacteristics and in which the first and second blocks are connectedtogether by a third acoustically transmissive material.

The material of the first and second blocks may be identical to thethird acoustically transmissive material or may have different acoustictransmission characteristics.

The third acoustically transmissive material may be air.

The present invention also provides means for supplying the first andsecond outer conductors with a first alternating current having a firstdefined amplitude and phase and means for supplying the first and secondinner conductors with a second current having a second defined amplitudeand phase both of which are different to the first alternating current.

The present invention also provides apparatus for supplying drivingcurrents for active acoustically controlled magnetic coils includingfirst coil current supply means for supplying to the magnetic coil afirst current at a first phase and second coil current supply meanssupplying to the magnetic coil a second if current at a different andvariable amplitude to the first current and at a second variable phasedifferent to the first phase.

The apparatus can alternatively provide pulsed driving currents ofsimilar waveform but delayed by a variable delay.

Preferably a phase splitter is provided to control the respective phasesof the first and second currents.

Preferably acoustic feedback is provided to monitor the sound emittedfrom the coil.

Preferably the coil system further comprises active magnetic screeningcoils

Embodiments of the present invention will now be described, by way ofexample, with reference to the accompanying drawings in which:

FIG. 1 shows a diagram representing two coupled line elements ofconductor, dl, of equal masses m carrying equal and opposite currents.The centre of mass of the system remains fixed if the spring constants,κ, are equal. The system is placed in a magnetic field B which givesrise to the forces F causing displacements.

FIG. 2 shows a rectangular conductor loop carrying a current I placed inmagnetic field B such that the loop plane is normal to B. All forces Fand F' are balanced,

FIG. 3 shows

(a) A diagram with two straight parallel wires lying in the same planecarrying currents I₁ and I₂. The wires are mechanically coupled with arigid block of material. The wire plane is arranged to be normal to themagnetic field, B, which is aligned with the z-axis.

(b) Plan view of the wire pair shown in (a) above. Lorentz forces F andF' squeeze the block, deforming it as indicated by the dotted lines, sothat sound, S, is emitted from the surface of the encapsulating solidalong the ± z-axis,

FIG. 4 shows a plan view of test coil comprising 2 rectangular loops ofwidth a and length b (see also FIG. 2). The coils are spaced a distancex apart. Planes of coils are parallel with B. Shading indicatesmechanical coupling between coils created by potting in resin. Thecurrents in each coil I₁ and I₂ are in general not equal and opposite;Note currents in conductors parallel with B produce no forces. Thelength of both coils along the y-axis is b (not shown),

FIG. 5A shows a sketch of the test coil experimental arrangement whichis driven from a Hewlett Packard network analyser via a phase splitterand independent Techron amplifiers providing separate currents I₁ and I₂(with relative phase φ) to the two coils. The acoustic output from thetest coil is picked up by a microphone and fed back into the networkanalyser.

FIG. 5B shows a block diagram of additional electronic equipmentrequired when operated in a pulse gradient mode,

The apparatus can alternatively provide pulsed driving currents ofvariable waveform and delayed by a variable delay.

FIG. 6 shows

(a) Graph of sound pressure level output I_(s) (dB) versus f for thetest coil arrangement of FIG. 5. The receiving microphone was placedapproximately 1 m from one face of the coil arrangement. The line is thetheoretical curve, Eq. [12], for α=θ=0 with 20 log ₁₀ A₁ =80 dB. Seetext for further details. The squares show experimental data when I₁=-I₂ The circles show slightly lower values of I_(s) when the phase isvaried from the 180° condition. The triangular points show even furtherreductions in I_(S). Δ¹ corresponds to an increase in current I₁ fromits initial value of 20 A, while Δ² corresponds to a decrease in currentI₂ from its initial value of 20 A. The Δ² points in general show agreater reduction in noise output as one would expect from the theory.

(b) Graph of the phase angle φ versus f for the circled data points.Once this phase had been found it was left unchanged for the subsequentvariations in amplitude of I₁ and I₂. The straight line is thetheoretical phase, Eq. [17]. See text for more details,

FIG. 7 is a diagram showing the plan view of the nth quartet ofrectangular current loops from a set of quartets arranged to produce amagnetic field gradient along the x-axis. Note all currents in thecentral wires of the nth quartet have the same sense. The length of thecoils along the y-axis is b_(n) (not shown),

FIG. 8 shows

(a) A diagram of a rectangular wire loop carrying current I₁ and secondre-entrant loop carrying current I₂. The outer and inner loops aresupported in a polymer matrix. The loop plane is arranged to be normalto the magnetic field B.

(b) A plan view of the wire loop arrangement of FIG. 8(a) above. Eachhalf of the loop arrangement is set in a polymer resin and part of thegap between each half is filled with the same material with a centralair gap or the whole gap is filled with a different material allowingmechanical coupling of each half of the loop assembly. As indicated thecurrents I₁ and I₂ in each half of the assembly are in anti-phase.

(c) An alternative mechanical coupling arrangement for each half of theplate allowing tensile as well as compressive net forces across the gap,

FIG. 9 shows a plan view of an assembly of double rectangular loops ofthe type shown in FIG. 8, which are arranged to form at region O amagnetic field gradient which is transverse to the static field B. Theouter loops of each quadrant carry a current I₁ and the inner re-entrantloops in each quadrant carry a current I₂. The conductors are set in asuitable polymer resin with either the same material with a central airgap or the whole gap is filled with a different material separating eachhalf of each quadrant,

FIG. 10 shows a plan view of assembly of mechanically coupledrectangular loops of the type shown in FIG. 4 carrying currents I₁ andI₂ as indicated. The assembly is arranged to produce at region O amagnetic field gradient which is transverse to the static field B,

FIG. 11 shows

(a) A side elevation view of a single quadrant of a gradient set of thetype indicated in FIG. 9 above but in which the rectangular loops aredeformed into closed arc loops as indicated. The outer arc loop carriescurrent I₁ and the inner Ha re-entrant arc loop carries current I₂.Because the outer loop is closed, I₃ =I₁. The conductors are set in asuitable polymer resin with either the same material with a central gapor a different material in the gap separating each half of eachquadrant,

(b) An end view of a concentric cylindrical transverse coil withdistributed windings of the fingerprint design which constitutes an openloop structure. Provided the coil build thickness t<<a, the meancylinder radius, the currents I₁, I₂ and relative phase φ are determinedaccording to Eq. [26]. The coil is supported in a polymer matrix. Wiredetails are shown inset together with the gap which is filled witheither the same material with a central gap or a different material.

FIG. 12 sketches showing the wire layout for the two geometries used toobtain experimental data. (a) The rectangular board layout. (b) Theclosed arc loop board layout. The board dimensions are shown on thediagrams. Each board was slotted with an air gap of 2 mm.

FIG. 13

(a) Sketch of a gradient set comprising many plates with spacers(shaded). The whole assembly is compressed under tension rods. Thespacing material is an acoustic absorbent such as rubber, Vulcanite orsomething similar.

(b) Sketch of one spacer showing an embedded counter-wound cooling tube,

(c) sketch of one y-gradient coil plate.

FIG. 14

(a) Sketch of current paths for an open loop acoustically controlledcoil section with different arc angles subtended at point O.

(b) Wire path for a closed arc loop coil section with an acoustic screenforming a re-entrant loop. A slot is cut along the dotted line AB.

FIG. 15 sketch of current paths for an acoustically controlled hoop ofradius a carrying current I₁ forming part of a z-gradient set. Theacoustic shield carries a current I₂ in a second hoop of radius bcoaxial and coplanar with the primary hoop. All wires are either insetor moulded into the board which is made of a suitable polymer resin. Thedotted line indicates the board mounting for the wires.

FIG. 16 Sketch of an alternative arrangement for acoustic control of aconducting hoop of radius a carrying a current I₁. The acoustic screencomprising wires at radii b, b' has a slot between the wires (dotted)with three support segments shown maintaining the integrity of the innerwire hoop currents ±I₂ flow through wires at radii b,b' respectively. Athird current -I₃ flows through the outer hoop of radius c. All wiresare either inset or moulded into the board which is made of a suitablepolymer resin. The inner and outer dotted circles represent the boardsupport dimensions.

FIG. 17

(a) Sketch showing integral magnetic screening and acoustic shielding ofa primary hoop of radius a carrying current I₁. The magnetic screen lieson a cylinder of radius c. The acoustic shield is placed between theprimary coil and the magnetic screen with currents ±I₂ on radii b,b'. Inbetween the acoustic shield wires is a continuous thin slot. Twodifferent support materials are used forming two concentric annularcylinders of radius and thickness a,x₁ and b',x₂ with characteristicsv₁, and v₂,α₂ respectively.

(b) Integral magnetic screening and acoustic shielding of a primarytransverse gradient coil of the fingerprint design (not shown). Theprimary coil and half of the acoustic shield are potted in an innercylindrical annulus. The magnetic screen and the other half of theacoustic shield are potted in an outer cylindrical annulus of differentmaterial to the inner annulus. The two cylinders are loosely coupled.

All wires are either inset into machined slots in the annular cylindersor moulded into them using suitable polymer resins.

FIG. 18. A graph showing the acoustic output intensity I_(s) versus ffor the rectangular board arrangement of FIG. 12a. The squarescorrespond to data when I₁ =-I₂. The curve is the theoretical expressionEq. [14] with θ=α=0. The triangles show the much reduced output when theacoustic shield is properly adjusted. The superscript 1 corresponds toI₁ =10 A with I₂ varied. The superscript 2 corresponds to I₂ =10 A withI₁ varied. These data indicate a residual attenuation which at somefrequencies is better than -10 dB, see Eqs. [31 and 32].

FIG. 19. Graph showing the variation of phase φ versus f correspondingto the data of FIG. 18.

FIG. 20. A graph showing the acoustic output intensity I_(s) versus ffor the arcuate segment arrangement of FIG. 12b. The squares correspondto data when I₁ =-I₂. The curve is the theoretical expression Eq. [14]with θ=α=0. The superscripts a and b refer to the board material,polystyrene or Perspex respectively. The triangles show the much reducedoutput when the acoustic screen is properly adjusted. The superscript 1corresponds to I₁ =10 A with I₂ varied. The superscript 2 corresponds toI₂ =10 A with I₁ varied. These data indicate a residual attenuationwhich at some frequencies is around 0 dB, see Eqs. [50 and 61].

FIG. 21. Graph showing the variation of phase φ versus f correspondingto the data of FIG. 20. The superscripts a and b refer to the boardmaterial, polystyrene or Perspex respectively.

FIG. 22. Sketch showing the side elevation (solid line) for an activemagnetically screened coil with primary radius a and magnetic screenradius b. Also shown in dotted lines are the positions of the acousticshields. The primary coil acoustic shield has a radius f and theacoustic shield for the magnetic screen has a radius F.

The invention will now be described with reference to the drawings.

Basic Principles

A conductor element l=lη carrying a current I placed in a uniformmagnetic field B=Bk, will experience a Lorentz force F=Fζ per unitlength given by

    F=Il×B=ζBI sin δ                          (1)

where δ is the angle between the conductor and the field direction andη, ζ and k are unit vectors which lie along the conductor direction, theforce direction and magnetic field direction respectively. When δ=0, F=0and when δ=90°, F is a maximum. If the conductor could be firmly fixedto an immoveable coil former so it did not move or flex when energised,no sound would be produced.

In a practical coil system the mass of the coil former can be increasedin the hope of making it effectively immoveable. But with high staticmagnetic fields and the very high currents now being used to generatethe gradients in high-speed imaging techniques, the magnetic forces areso large that it is impossible to create an effectively immoveable mass.

In its simplest form the active force balance approach utilises a pairof mechanically coupled straight parallel wires carrying equal andopposite currents. The arrangement is shown in FIG. 1 for a pair of wireelements, each of mass m, coupled by springs of coupling constant κ. Theplane through the wires is arranged to be normal to the field B.

Active force balanced coils

Using the above-active force balance principle we consider a rectangularloop of conductor carrying a current I and placed in a magnetic field B,FIG. 2. Provided that the plane of the coil loop is normal to the Bfield direction, all forces F,F', in the conductors are equal andopposite for any sense of the current I. If these forces are coupled vianon-compressive struts and ties, all net forces in the system arebalanced. In addition all moments, couples and therefore torques arecancelled.

It is clear that if non-compressive materials are used, the conductorsthemselves cannot move. In this case no sound will be generated in sucha coil arrangement. Of course the whole coil structure can be flooded orpotted with a suitable plastic resin or recessed into a block ofmaterial to replace the individual struts and ties by effectively acontinuum of struts and ties.

Compressive Struts

All solid materials have visco-elastic properties. This means that thenoise cancellation described above will have some limitations insofarthat there will be some residual movement of the conductors. Suddenmovement of the conductors will send a compressional wave with aprogressively attenuated amplitude through the material. The velocity ofsuch a wave v is given by ##EQU1## where E is Young's modulus and p isthe density of the material. The velocity and wave length λ are relatedby

    v=fλ                                                [3]

where f is the frequency of the propagated wave.

Acoustic Control Theory

For simplicity we consider two straight parallel wires spaced a distancex and mechanically coupled by a block of length b, FIG. 3a. We considergeneralised compressive/expansive displacements of the block at thepositions of the two wires. We consider the case when wires are drivenby currents of amplitudes I₁, I₂ and with a phase difference φ. Eachwire launches a plane acoustic wave in the solid. The waves give rise toa net transverse acoustic source amplitude A_(S) at the wire positionsgiven by

    A.sub.S =A.sub.1 e.sup.iωt e.sup.ikx e.sup.-ax +A.sub.2 e .sup.i(wt+φ)                                          [ 4]

where A₁ and A₂ are the initial wave amplitudes at each wire positionwhich are proportional to I₁ and I₂ respectively, ω=2πf in which f isthe applied frequency of the driving current in the coil, k is the wavepropagation constant in the polymer block given by

    k=2πf/v                                                 (5)

and α is the wave attenuation per unit length. We assume that thistransverse motion gives rise to wave propagation, S, of related form toEq. [4] along the z-axis, through the transducer action of the block assketched in FIG. 3b. Acoustic measurements can be made with either oneor both wires powered. For just one wire the unscreened acoustic sourceamplitude A_(S1) is given by

    A.sub.S1 =A.sub.1 e.sup.2iπft,                          [6]

where in general A₁≠A₁ because of potential macroscopic translations ofthe block. Let the phase φ be split into two components given by

    φ=π+θ.                                        [7]

Let us now write the amplitude A₂ as

    A.sub.2 =A.sub.1 e-β                                  [8]

where β is real number such that the factor e⁻β is an attenuation term.Because A₁ ∝ I₁ and A₂ ∝ I₂ we may write the current I₂ as

    I.sub.2 =I.sub.1 e.sup.-β.                            [9]

Since I₂ is under experimental control, variation of I₂ effectivelyintroduces a non-zero value of β. Using Eqs. [7] and [9] we rewrite Eq.[4] as

    A .sub.S =A.sub.i e.sup.iωt (e.sup.ikx e.sup.-αx -e.sup.iθ e-β).                                [10]

When β=αx and by changing the phase such that θ=kx, it is possible tomake A_(S) =0. Both θ and β are experimentally accessible quantities.The above conditions which make Eq. [10] vanish constitute the newprinciple of active acoustic control. In the special case that β=αx onlyEq. [10] gives ##EQU2##

The emitted sound intensity in decibels, I_(S), for this arrangement istherefore proportional to

    I.sub.S =20 log.sub.10 {2 A.sub.1 e.sup.-αx sin [(kx-θ)/2]}.[12]

The emitted sound intensity in decibels for a single wire is

    I.sub.So =20 log.sub.10 [A.sub.1 ].                        [13]

The relative attenuation, A, of the emitted sound intensity in decibelsis therefore given by ##EQU3##

Thus for a given v and f, θ can be chosen to give an infinite value ofthe relative noise attenuation of emitted sound intensity. We point outthat in addition to θ in Eq. [14] there are many other values which willsatisfy the condition of infinite attenuation. For example θ±nπ willalso satisfy the condition. We return to this point later in theexperimental section. Of course, if α is itself a function of frequency,it will be necessary to adjust β for each value of f.

Theoretical Phase

If the sound propagation velocity, v, in the solid material isindependent of frequency, a sound pulse initiated on one side of thesolid will arrive at distance x delayed by a time interval τ given by

    τ=x/v.                                                 [15]

The corresponding phase delay for the assembly at frequency f whichmakes Eq. [14] vanish is therefore

    θ=+ωτ±nπ=+2πfτ±nπ.      [16]

Thus θ is proportional to f and is zero for f=0. Substitution into thetotal phase φ, Eq. [7], gives

    φ=π(1±n)+2πfτ.                            [17]

In our case due to hardware limitations n can take on only the valuesn=0, ±1, giving three equations which describe the phase variation withfrequency.

The introduction of this new principle of active acoustic control meansthat the choice of polymer resin or support material is less critical.Complete compensation of both wave propagation phase and waveattenuation is now possible.

Experimental Arrangement

In order to test the theory developed in §5 above, a test coilarrangement was made comprising two parallel flat rectangular coils eachcapable of being driven independently from its own current source withcurrents I₁ and I₂. The arrangement is shown in plan view in FIG. 4. Theshaded regions in FIG. 4 were potted in solid polystyrene so as toencase the active current carrying wires. The wires in each end sectiontherefore behave as a parallel pair corresponding to FIG. 3a. The secondpotted pair of wires is part of the current return path for eachseparate coil. Because of the geometrical arrangement, currents flowingalong the direction of B experience no Lorentz forces. Sound, S, isemitted along a direction normal to each block face as indicated.

The coils were constructed with 10 turns of wire each, with coildimensions a=40 cm and b=40 cm. The two coils were mounted coaxiallywith their planes parallel to B and spaced 7.5 cm apart.

The block diagram circuit of FIG. 5a shows the experimental arrangement.It comprises a Hewlett Packard network analyser (HP8751A) which providesan AF source and received signal display. The AF output is fed via aphase splitter to two Techron amplifiers. The phase splitter providestwo low voltage AF signals of independently adjustable amplitude andrelative phase, i.e. V₁,φ₁ and V₂,φ₂. The Techron outputs are fedseparately to each coil of the test assembly. The test assembly isplaced in a magnetic field with the field along the direction indicatedin FIG. 4.

Sound emitted from the test coil is picked up with an electretmicrophone (type RS 250-485) centrally placed (point P of FIG. 4) atabout 1 m from the emitter surface. The microphone output was fedthrough a 20 dB gain preamplifier back to the network analyser input R.The network analyser was also used, via its A and B inputs, to monitorthe current amplitudes and phase.

For operation in a pulsed mode the circuit of FIG. 5b is insertedbetween points P,P' and Q,Q' of the circuit of FIG. 5. In thisarrangement switches S₁ and S₂ switch out the phase splitter input andswitch in the pulse generators PG1 and PG2 which for non-dispersive wiresupport materials produce shaped output pulses of independently variableamplitudes and shapes. These now form the input signals to the gradientdrive amplifiers. Each pulse generator is triggered via adjustabledelays D1 and D2 with respect to a common trigger input T FIGS. 5(a) and(b). In general D1 can be set to zero and D2 varied together with thepulse amplitude of PG2 to minimise the acoustic noise output. Foracoustically dispersive coupling materials it is necessary to monitorthe wave shape arriving at the far side of the support block. Thiswaveform is then used to generate the amplitude and shape of the outputwaveform of PG2.

Experimental Results

FIG. 6(a) shows experimental acoustic noise output data when both coilsare supplied with sinusoidal currents under a range of conditions. Thesquare data points were obtained when I₁ =-I₂ =20 A. The theoreticalcurve, Eq. [12], is also plotted for the case α=0 and θ=0 with 20 log₁₀A₁ =80 dB, V=0.975×10³ ms⁻¹ and x=0.075 m. The value of v was chosen foroptimum fit. Calculated values of v for polystyrene lie in the range(1.15-2.02)×10³ ms⁻¹. The points □^(a) are rogue data due to Chladniresonances or structural buckling modes. They are included forcompleteness but are irrelevant to compressional wave theory.

The circular data points were obtained by varying the phase θ from the180° condition to give a minimum noise output. The experimental phase isshown in FIG. 6(b). The straight line is the theoretical phase, Eq.[17], with τ=83 μs corresponding to a sound velocity v=0.9 kms⁻¹ in theblock. Further reduction in noise output was obtained by varying theamplitude of either I₁ or I₂. This is equivalent to introducing anon-zero value of β in Eqs. [9] and [10]. These results correspond tothe triangular data points. Referring to Eqs. [9 and 10] we see thateither I₂ can be decreased or I₁ increased to make A_(S) =0 when θ=kx.That is to say, the ratio I₂ /I₁ =e⁻β can be achieved in two ways forfixed β. The superscript 1 refers to an increase in I₁ for I₂ =20 Awhereas the superscript 2 refers to a decrease of I₂ when I₁ =20 A.While all triangular points show a considerable noise reduction, asexpected the Δ² points give the best results.

The experimental procedure was to set phase first and then adjustamplitude. A better approach, not followed in this Section but usedlater is to iterate the procedure in order to optimise the overall noiseattenuation performance. One surprising feature of the data is thedramatic noise reduction of ˜40 dB at around 5.5 kHz. This frequencycorresponds approximately to half-wavelength resonance of the block,where sound output is normally a maximum. The large changes in acousticoutput support the theoretical predictions of Eq. [14] and confirm theessential correctness of our approach. We note that for a loss-lessmaterial, A would peak periodically at higher frequencies. Thisbehaviour has not been observed in our experiments using polystyrene asthe potting material because α≠0. Indeed, from the measured values of βusing Eq. [9] we find a small variation of α with frequency as follows:f=2.0 kHz, β=0.28, α=3.76 m⁻¹ ; f=3.0 kHz, β=0.47, α=6.26 m⁻¹ ; f=5.5kHz, β=0.21, α=2.76 m⁻¹.

Gradient Coils

General Principles

For simplicity, we shall consider gradient coils made up of pairs offinite length straight wire sections essentially as shown in FIG. 3. Thesmallest number of conductor pairs to form a transverse gradient coil is4. The first quartet of pairs in a set of n quartets is shown in FIG. 7.The current in all 4 inner wires must have the same sense for either aG_(X) (shown) or G_(Y) arrangement. The gradient field is the sum ofmagnetic fields from all 8 wires. We shall consider one wire of onequadrant of the quartet to carry a current I₁. For active acousticscreening of this wire we require a second wire carrying a current I₂and mechanically coupled to the first, see FIG. 3. The z-component ofmagnetic field B_(P) (x,y,z) at a distant point P(x,yz) is given (V.Bangert and P. Mansfield, Magnetic field gradient coils for NMR imaging.J. Phy. E. Sci. Instrum., 15, 235-239 (1982) by

    B.sub.P =-(μ.sub.o /4π)((x-D.sub.1)g.sub.1 I.sub.1 -(x-D.sub.2)g.sub.2 I.sub.1 e.sup.-β e.sup.iθ)e.sup.iωt.[18]

where

    D.sub.1,2 =A.sub.1,2 tan ε.sub.1,2                 [ 19]

and ##EQU4## where Y_(W) is the distance along the wire and A₁,2 are thenormal distances of the wires to the y-axis (see FIG. 3). The anglesε₁,2 are defined in FIG. 3. When θ=0 in Eq. [18] the magnetic field at Pfrom the first wire is reduced by the negative field from the second.However, at a frequency sufficiently high to make the connecting blockresonate at λ/2, θ=π. In this case the two currents become in-phase andmagnetic fields for each wire now add. This will have importantimplications in some quiet gradient coil designs by increasing theirefficiency.

Practical Gradient Arrangements

The principles of active acoustic control can be immediately applied tothe design of gradient coils (P. Mansfield, B. Chapman, P. Glover and R.Bowtell, International Patent Application, No. PCT/GB94/01187; PriorityData 9311321.5, Jun. 2, (1993). (P. Mansfield, P. Glover and R. Bowtell,Active acoustic screening: design principles for quiet gradient coils inMRI. Meas. Sci. Technol. 5, 1021-1025 (1994). (P. Mansfield, B. L. W.Chapman, R. Bowtell, P. Glover, R. Coxon and P. R. Harvey, Activeacoustic screening: Reduction of noise in gradient coils by Lorentzforce balancing. Magn. Reson. Med. 33, 276-281 (1995)). As discussedabove we can design a transverse gradient coil from four or morerectangular loops as indicated in plan view for FIG. 7 to produce an xgradient, G_(X). In this arrangement each quartet of loops has a widtha_(n), length b_(n) and comprises N_(n) turns of conductor. The currentin successive quartets of loops is equal to I_(n). The plane separationfor the nth quartet is 2z_(n) and the in-plane loop displacement isa_(n) +X_(n). In such a coil arrangement the forces and torques cancel.A spatially more uniform magnetic field gradient is achieved with n>1.

Because most whole-body imaging systems use cylindrical static magneticfield symmetry, the rectangular loops described in FIG. 7 can of coursebe deformed into arcs. Provided the arcs form closed loops, the planesof the loops are normal to the magnetic field B, and provided the coilwires are mechanically coupled by struts or by potting in a resin, alltorques and forces balance just as in the case of a rectangular loop.This result is true for any closed loop carrying a current I which isconfined to a plane and where δ=90°, Eq. [1], since the line integral ofthe Lorentz force around the loop ##EQU5##

This result can be generalised to line integrals where the current inthe loop varies, i.e., ##EQU6## where I_(i) is the current flowing inthe ith segment of the contour. In this form force balance is achievablewith open current loops. The test coil arrangement of FIG. 4 is anexample of an open current loop, Eq. [22], where the return currents arezero in the x-y plane. We emphasise however that for active acousticcontrol, the line integral, Eq. [22] does not vanish, a feature whichdistinguishes the present invention from the prior art.

New gradient Coil Arrangements

From the new principle of active acoustic control which utilises currentamplitude and phase adjustment, we construct a flat rectangular coilarrangement which comprises an outer closed loop carrying a current I₁and an inner re-entrant narrower loop carrying a current I₂ as shown inFIG. 8a. In a first embodiment both loops are supported by a polymermatrix as indicated in FIG. 8b. The supporting matrix material is splitcentrally and the gap filled as shown in FIG. 8b. The material in thegap is preferably another polymer or rubber. In order to maintain theintegrity of the two halves of the plate assembly, an alternativecoupling of the plates is shown in FIG. 8c. This arrangement ensurescoupling under both tensile and compressive forces. Seen in plan view,FIG. 8b, each half of the plate looks like a separate coil. However, thedistinguishing feature over prior art is that I₁ ≠-I₂ because of bothphase and amplitude. The net effect of this is that overall the Lorentzforces within each half of the plate do not balance. However, the forcesof both halves of the assembly do balance. Wave propagation within eachhalf of the assembly is quenched provided |I₁ /I₂ | and the relativephase are chosen properly. Each half of the plate assembly moves inunison compressing or stretching the coupling material. Since the gap isarranged to be narrow, wave propagation phase effects across the gap areeffectively negligible for most coupling materials.

In a second embodiment as shown in FIG. 8A two blocks of material BL1and BL2 are used to maintain the mechanical integrity of the two halvesof the coil assembly. The blocks can be the same as the supportingmaterial. The remaining gap can be an unfilled air gap.

The new rectangular plate units can be built up to form transversegradient sets as shown in FIG. 9. That is to say each quadrant of thequartet of rectangular coils shown in FIG. 7 is now replaced by theclosed loop arrangement shown in FIG. 8.

The basic test coil arrangement of FIG. 4 can also be used to make agradient set as shown in FIG. 10. However, the net Lorentz forces withineach quadrant of this arrangement are not zero. This arrangement wouldtherefore generate large bending moments overall.

Finally, the new principle of active acoustic control can be applied tocylindrical coil geometries. For example, the rectangular coils can bedeformed into arcuate units one of which is shown in FIG. 11a. Theseunits in turn can be used as the basic building block for transversegradient coil assemblies. Other cylindrical geometries include thedistributed transvese gradient designs of which the fingerprint coil isan example. In this arrangement two pairs of coils are arranged as inFIG. 11b.

Deformation of straight wires into arcs means that Eq. [10] no longerholds since, for a common angular displacement, the wire lengths ondifferent arc radii are not equal. The radius of the inner wire arc is aand carries a current I₁. The radii of the middle pair of wires are band b' and carry currents ±I₂ and the radius of the outer wire is c andcarries a current -I₃. The important feature is that the Lorentz forcesare balanced between the cylinders. The Lorentz forces are allproportional to the product of current and arc length. Let the Lorentzforces at the arc radii of FIG. 11(b) be F_(a), F_(b), F_(b), and F_(c).If the inner pair of coils is closely spaced, we may take F_(b) equal toF_(b), without appreciable error.

Provided the radial build of the coil arrangement, t<<a, the averageradius of the coil assembly, we may assume plane wave transmission ofthe acoustic wave between cylinders. In this case Eq. [4] may berewritten for the two open loop sections as

    A.sub.S =e.sup.iωt [(A.sub.a e.sup.ikr.sbsp.1 e.sup.-ar.sbsp.1 +A.sub.b e.sup.iφ)+(A.sub.b,e.sup.iφ +A.sub.c e.sup.ikr.sbsp.2 e.sup.-αr.sbsp.2)]                                  [23]

where A_(a), A_(b), A_(b), and A_(c) are the initial wave amplitudes ateach wire position. The Lorentz forces on each wire arc are given by

    F.sub.a =aψ.sub.a I.sub.1 ; F.sub.b =F.sub.b, =±bψ.sub.b I.sub.2 ; F.sub.c=-cψ.sub.c I.sub.3 ;                         [24]

where ψ_(a), etc., are the angular displacements of the arcs. In thefollowing we take these displacements to be all equal to the azimuthalangle ψ. The wave amplitudes in Eq. [23] are all proportional to theirrespective Lorentz forces, i.e.

    A.sub.a =ΛF.sub.a, etc.,                            [25]

where Λ is a constant. Making these substitutions in Eq. [23]

we obtain ##EQU7##

If we now take r₁ =r₂ =r and let φ=π+θ, Eq. [7], Eq. [26] then becomes

    A.sub.S =Λψ[aI.sub.1 (e.sup.ikr e.sup.-αr -e.sup.-β1 e.sup.iθ)-cI.sub.3 (e.sup.ikr e.sup.-ar -e.sup.-β.sbsp.2 e.sup.iθ)].                                         [27]

where we have substituted bI₂ /aI₁ =exp (-β₁) and bI₂ /cI₃ =exp (-β₂).We choose kr=θ which then allows the phase term to be factored out. Wealso note that since |F_(a) |=|F_(c) |, aI₁ =cI₃ for constant arc angle.This means that β₁ =β₂ =β. Finally by choosing β=αr, the wholeexpression, Eq. [27], can be made to vanish.

In the arrangement of FIG. 11b the inner pair of coils at radii b, b'plays the same role as the re-entrant narrow loop in a straight set ofLorentz force balanced conductors. The gap between the inner pair ofcoils is filled with a coupling material which is preferably differentto the general supporting polymer potting material. The same principlecan be used to form acoustically controlled single arc and distributedarc saddle geometry transverse gradient coils.

In all the above conductor arrangements the arc loops may be connectedin either a series or a parallel arrangement or a combination of both.In all cases the connections to the arcs must be made in such a way thatthe feeder and connector wires or conductors are in pairs runningparallel with the main magnetic field B and preferably set in a plasticresin in the final wiring arrangement.

Magnetic Screening with Active Acoustic Control

Acoustically controlled coils can also be magnetically screened tocircumvent the eddy current problem using the principles of activemagnetic screening introduced by Mansfield and Chapman ((P. Mansfieldand B. Chapman, Active magnetic screening of gradient coils in NMRimaging. J. Mag. Res. 66, 573-576 (1986), (P. Mansfield and B. Chapman,Active magnetic screening of coils for static and time-dependentmagnetic field generation for NMR imaging. J. Phys. E. 19, 540-545(1986)). Several ways of doing this are possible by adding extramagnetic screening coils to the assembly. General details are describedelsewhere ((P. Mansfield, B. Chapman, P. Glover and R. Bowtell,International Patent Application, No. PCT/GB94/01187; Priority Data9311321.5, Jun 2, (1993), (P. Mansfield, P. Glover and R. Bowtell,Active acoustic screening: design principles for quiet gradient coils inMRI. Meas. Sci. Technol. 5, 1021-1025 (1994)) and would be obvious toone skilled in the art.

Pulses

We have discussed so far the situation when gradients take the form ofcontinuous modulated sine waves. However, there are many applications inimaging where pulse gradients are required. We consider a square pulsewith a ramped leading edge which is applied to the test coil. For anacoustically non-dispersive support block application of I₁ will launcha wave through the material at time t and arrive at the other side ofthe block at time t+τ. The application of I₂ should therefore be delayedby τ with respect to I₁ in order to balance the Lorentz forces. Anexperimental arrangement for achieving this is shown in FIGS. 5a and b.

If the pulses are in the form of a regular sequence of trapezoids, thetrapezoidal waveform for I₁ (t) may be represented by a Fourier sequenceof the form (P. Mansfield, P. R. Harvey and R. J. Coxon, Multi-moderesonance gradient coil circuit for ultra high speed NMR imaging. Meas.Sci. Technol. 2, 1051-1058 (1991).

    I.sub.1 (t)=I.sub.o Σa.sub.n sin nωt,          [28]

where a_(n) is the amplitude of the nth Fourier harmonic, n is theharmonic number and ω is the angular frequency of the fundamental mode.The values of n in this instance will be odd integers i.e. n=1,3,5 . . .In order to properly effect active acoustic control, I₂ (t) should havethe form

    I.sub.2 (t)=I.sub.o Σa.sub.n sin (nω+θ.sub.n),[29]

where θ_(n) is the phase delay for the nth mode. It will be seen thatθ_(n) can also be chosen to maintain the rise and fall times of thepulse thereby maintaining its shape.

For a dispersive medium the leading and trailing edges of the secondwaveform will be delayed in time and accordingly shaped to fit the wavepropagation properties characteristic of the mechanical couplingmaterial by matching the waveform to that arriving on the far side ofthe material block through which the acoustic wave is travelling.

Discussion

An important consideration in the extension of active acoustic controlin gradient coil design is acoustic shielding efficacy. The greater theacoustic attenuation achieved the less likelihood the whole concept willbe vitiated when coil current is increased to make up gradient amplitudeshortfall due to the active acoustic control.

In earlier attempts to design quiet coils, it was concluded thatgradient coil wires should be supported by materials in which thecompressional wave velocity, v, was high. It was also considereddesirable that the wave attenuation per unit length, α, be ideally zero.

In the present invention both of these constraints are effectivelyremoved by splitting each closed loop into two loops which are separatedby either by a small air gap or a small gap coupled by a material ingeneral different and softer than that of the plates themselves. In oneembodiment the inner wires carrying current I₂ form a re-entrant narrowloop within the larger loop carrying current I₁. The proximity of theinner loop wires means that their magnetic field contribution outsidethe outer loop is effectively zero. In the new arrangement, both theamplitude and phase of I₁ and I₂ are variable to provide the optimumnoise reduction.

In addition to gradient coil designs based on closed arc loops,re-entrant loops, rectangular loops and rectangular re-entrant loops,etc., the new principle of active acoustic control can be applied toconcentric cylindrical transverse gradient designs of the fingerprintvariety as well as to distributed z-gradients.

In all the above new coil arrangements it would mean that within thecommonly used frequency range (1.0-3.0 kHz) for Echo Planar (EPI) andEcho Volumar (EVI) imaging (P. R. Harvey & P Mansfield, Echo VolumarImaging [EVI] at 0.5T: First Whole Body Volunteer Studies. Magn. Res.Med. 35, 80-88 (1996)), additional acoustic attenuation of between 10-25dB is readily obtainable making a total attenuation of between 30-50 dBachievable.

Further Embodiments

Effect of Drive Wires

The above analysis assumes that the current drive circuit adds noacoustic noise. If this were the case measured values of A would beinfinite. As we shall see from the experimental section, this is not thecase. The achievable attenuation is limited by extraneous soundgenerated by the current supply leads to the coil.

Let the amplitude of the extraneous sound A_(es) be

    A.sub.es =e.sup.iωt A.sub.e.                         [30]

This should be added to Eq. [11]. The result of this is that Eq. [11]now becomes ##EQU8##

When the sine term vanishes the attenuation becomes

    A=-20log.sub.10 (A.sub.e /A.sub.1).                        [32]

Thus Eq. [32] shows that the drive bus arrangement and not the coildetermines the largest attenuation achievable. Careful construction andgeometrical placing of the drive bus can reduce A_(e) so that theresidual attenuation is of the order of 50-60 dB.

Slotted boards

So far we have considered the possibility of filling the machined slotswith a material which is in general different to the board material. Wenow consider the alternative possibility of simply leaving an air gap.This has advantages in that both halves of the board arrangement canmove independently and in particular each half can take up a vibrationalmode which is anti-phase to the other half. Inserting a hard material inthe slot would inhibit this mode. Provided each half of the boardmaintains its positional integrity an air gap can be left. FIGS. 12a and12b show two such arrangements, one for a rectangular re-entrant coilarrangement, the other for a re-entrant closed arc loop arrangement.

Total coil assembly

We have considered at length variations of the arc loops which wouldcomprise a coil assembly. But we have not so far discussed the stackingarrangement for such an assembly. It is assumed throughout this workthat acoustic noise is emitted from the flat faces of the boardssupporting the arc loops or the rectangular loops, these being placed ina plane normal to the magnetic field. Of course in an ideal arrangementof plates no sound would be emitted along the field axis. However, theremay well be residual sound levels emitted and in order to absorb thesethe coil support plates are spaced by rubber or suitable plasticabsorbent material which is sandwiched between the plates as shown inFIG. 13 (a) and (c) with the requisite variable spacing to produce theoptimum magnetic field gradient. As well as absorbing any residual soundemitted from the plate surfaces, provided the plate stack is boltedtogether, such an arrangement will reduce considerably the possibilityof buckling modes or Chladni resonances occurring.

Plate spacers and coil cooling

Spacer plates 134 will be required to maintain a rigid structure. Thesecould be moulded rubber or plastic chosen for good acoustic absorption.The spacer plates would, in general, include flat pancake type coolingtubes 138 to dissipate heat from the adjacent coils. The wholearrangement would be pulled together by long non-metallic bolts. Anarrangement is shown in FIGS. 13a and 13b.

Sound propagation in a flat annulus or in an arc section of an annulus

In all the analysis given previously we have assumed implicity that wavepropagation in an annulus can be approximated by the plane waveexpressions derived for the rectangular plates.

The wave equation in Cartesian coordinates for sound propagation in asolid of bulk modulus M_(B) and density ρ is given by ##EQU9## whereA(x,y,z,t) is the amplitude of the sound wave passing through thematerial and where the velocity of the wave v is equal to √(M_(B) /ρ).NB For a thin flat sheet of material we can replace M_(B) by Young'smodulus E. The solution of the wave equation can best be achieved byusing the method of separation variables, in which case the generalsolution is given by

    A(x,y,z,t)=A.sub.o e.sup.ik.rt e.sup.iωt             [34]

where ##EQU10## describes the allowable vibrational modes of thematerial block, subject to the boundary conditions of zero amplitude atthe block faces and in which p,q,s are integers and L_(X),L_(Y) andL_(Z) are the dimensions of the block of material,

    k=ik.sub.X =jk.sub.y +kk.sub.z                             [36]

and

    r=ix+jy 4 kz.                                              [37]

For one-dimensional propagation Eq. [34] reduces to the results alreadyquoted previously. For a three-dimensional slab of material in which thewave amplitude along the z-axis is constant, we have

    A(x,y,t)=A.sub.o e.sup.ik.sbsp.x.sup.x e.sup.ik.sbsp.y.sup.y eiωt.[38]

Because of the orthogonality of the wave solutions, propagation alongthe x-axis and the y-axis are independent with wave solutions similar tothose used previously. There we have assumed that the wave amplitudealong the y-axis is constant. This situation obtains if the dimension ofthe slab of material along the y-axis is much greater than thex-dimension.

By choosing the slab of material to be rectangular, one can effectivelysuppress propagation along the long axis thereby concentrating onpropagation along the short axis or x-direction. This is what we haveimplicitly assumed in interpreting the experimental results for arectangular sheet.

We now turn to the general solutions of the wave equation in cylindricalpolar coordinates. We choose cylindrical polar coordinates because thegeneral shape of many common gradient coil structures have cylindricalsymmetry along the magnetic field axis for typical superconductivemagnets currently used for medical imaging.

In cylindrical polar coordinates the wave equation is ##EQU11##

Apart from the coordinate changes, the symbols A and v have the samemeaning as above. In this equation r is the radius measured in adirection orthogonal to the cylindrical axis, ψ is the azimuthal angleand z is the position coordinate along the cylindrical axis. Equation[39] can also be solved by the method of separation of variables. Wechoose the three orthogonal solutions to Eq. [39] as Z(r), Θ(ψ),F(z).The general solution of Eq. [39] is therefore

    A(r,ψ,z,t)=Z.sub.l (r)Θ(ψ)F(z)e.sup.iω.[ 40]

By substituting into Eq. [39] and dividing by A(r,ψ,z,t) we obtain##EQU12##

Since the functions are independent of each other we can solve each partof this equation separately. When this is done Eq. [41] becomes##EQU13## where we have put

    F"/F=-m.sup.2                                              [ 43]

and

    Θ"/Θ=-l.sup.2                                  [ 44]

with K=√(k² -m²). In this case Z_(l) (Kr) comprises the class ofcylindrical functions, Θ(ψ)=e.sup.±ilψ and F(z)=e.sup.±imz, so that thecomplete solution is given by

    A(r,ψ,z,t)=A.sub.o Z.sub.l (Kr)e.sup.±ilψ e.sup.±imz e.sup.iωt.                                          [45]

The constants l, m are integers, that is to say, l=0,±1, ±2, . . . andm=0,±1,±2, . . . . We shall see below we are concerned only with valuesof l=0,±1. The value m=0 corresponds to a radial acoustic wave which hasconstant amplitude along the z-axis. In the present invention weconsider propagation of radial waves in a thin slice of the material sothat we can take m=0 for most of what follows.

Since most actual gradient coil designs correspond to wires formed on anannulus of suitable material or on a segment of an annulus, we shall beconcerned with three values only of l, namely for a complete annulus l=0and for a segment of an annulus l=±1.

The angular solution for l=0 corresponds to a radial wave with no polarangle variation. This situation obtains when considering z-gradientcoils or Maxwell coils. The general solution of the radial part, Eq.[42], Z_(l) (kr), includes the Bessel functions of the first kind B_(l)(kr), the Bessel functions of the second kind Y_(l) (kr), also known asthe Neumann functions, N_(l) (kr) and Bessel functions of the third kindH_(l).sup.(n) (kr), or the Hankel functions of the first and second kindwhere n=1,2 respectively. For kr large the Hankel functions have theconvenient property that they turn into weighted exponential functions,namely ##EQU14##

It is noted that the difference between l=0 and l=±1 in the Hankelsolutions is simply a phase shift. It is also noted that the waveamplitudes reduce as 1/√(πkr/2). In other respects the solutions aresimilar to the plane wave solutions in a rectangular sheet of material.We also note that the condition for the approximate Hankel solutions toapply is that kr is large so that we can deal with either largestructures at relatively low frequencies or small structures at highfrequencies. For situations which do not satisfy these conditions, it isnecessary to revert to the Bessel functions of the first and/or secondkind, or the exact Hankel functions. These are given by the identity

    H.sub.l.sup.+,- (kr)=J.sub.l (kr)±iY.sub.l (kr),        [48]

where + and - refer to Hankel functions of the first and second kindrespectively. Equation [48] can be written as

    H.sub.l.sup.± (kr)=R.sub.l (kr)e.sup.±iθ.sbsp.l.sup.(kr)[ 49]

in which θ_(l) ≠kr but can be calculated from

    tan θ.sub.l (kr)=Y.sub.l (kr)/J.sub.l (kr)           [49a]

and where

    R.sub.l.sup.2 (kr)=J.sub.l.sup.2 (kr)+Y.sub.l.sup.2 (kr).  [49b]

For small values of kr, therefore, the phase variation with frequencywould not necessarily be linear but modified according to Eq. [49a].

In a manner similar to that used previously, we may write the amplitudeterm in Eq. [49] as

    R.sub.l (kr)=e.sup.-γ.sbsp.l.sup.(kr)                [ 49c]

where γ_(l) (kr) is simply equal to -lnR_(l) (kr). We note that theexact Hankel functions diverge at the origin through the divergence ofthe Neumann functions. However, since we are dealing with an annulus orannular segment, solutions will not include the origin. Thus we are freeto use the Hankel functions or their approximate forms, Eqs. [46,47]. Inthis work, however, the dimensions and frequencies used allow the abovementioned approximate Hankel solutions.

Modification of plane wave cancellation to include cylindrical solutions

Using the above theory we are now in a position to modify our previousresults for rectangular boards to give approximate solutions when thewires are in the form of an arc or a circle. Using the approximateHankel solutions we may now rewrite Eq. [23] as ##EQU15## where we notethat for arc segments l=1. In this expression we have included the arcangles ψ₁, ψ₂ and ψ₃. There are two cases to consider. The first is thatall angles are equal. The wire arrangement is shown in FIG. 14a. In thiscase both halves of Eq. [50] may be made to vanish simultaneously whenthe phase terms are equalised, ie when kx=θ and for ##EQU16## with n=0,1and when the amplitudes are given by ##EQU17##

In order to satisfy these two conditions simultaneously we require that

    I.sub.1 a=-I.sub.3 c.                                      [54]

In this case the ratio of currents may be adjusted so that ##EQU18## sothat finally ##EQU19##

We note that three currents are required for this solution, I₁, I₂ andI₃ =(a/c)I₁.

The second case is for a closed arc loop as shown in FIG. 14b. In orderto maintain the integrity of this arrangement, slot AB (dotted) mustleave some material at each end. This will complicate the wavepropagation pattern and quench the radial vibrational modes at each endof the slot. We therefore ignore the wedge ends assuming that anyvibrational modes of these will be at considerably differentfrequencies. In this case the arc angles ψ₁, ψ₂ and ψ₃ are alldifferent. Both halves of Eq. [50] will have simultaneously zerosolutions when the phase terms are equalised and when ##EQU20##

If we take aψ₁ =bψ₂ =cψ₃ and set I₁ =-I₃ =I, both Eqs. [57 and 58] canbe satisfied giving ##EQU21##

If we now let ##EQU22## we obtain finally that ##EQU23##

As a general comment concerning the position of the slot AB; in FIG. 14bit has to lie along an anti-nodal line when resonated in the fundamentalmode before the slot is cut.

We now turn to the design of z-coils. Cylindrical z-coils comprise adistribution along the z-axis of conducting hoops, the planes of whichare normal to the z-axis. We shall, therefore, consider acousticscreening of a single hoop. There are in fact three cases to beconsidered. Type 1 is shown in FIG. 15 where we have two concentrichoops 151,152 carrying currents I₁ and I₂. Because the angles subtendedby both arcs are equal, ie ψ_(a) =ψ_(b) =2π we have from effectively onehalf of Eq. [50] with l=0, ##EQU24##

For kx=θ, and when

    φ=π-θ±nπ                                [63]

with n=0,1, Eq. [62] may be made to vanish when ##EQU25## which gives##EQU26##

The problem with the type 1 arrangement is that the field at the centreof each screened hoop includes contributions from I₂ which do not havethe same phase angle as I₁. This may be considered an undesirablefeature but can be overcome using the type 2 arrangement as shown inFIG. 16. Here we have a slotted arrangement with 3 currents I₁,I₂ andI₃. If the slots 153,154,155 are not continuous around the hoop then ψ₁≠ψ₂ ≠ψ₃ for each segment. In this case we may set I₃ =-I₁ provided thatψ_(n) are chosen such that for the three segments 2πa=3ψ₂ b=3ψ₃ c. Inthis case the condition for the acoustic sound output to vanish issimilar to that for the closed arc loops.

In the type 3 arrangement we consider the case that all arc angles areequal. In this case there is no support for the inner coil in FIG. 16.For this situation the condition that both halves of Eq. [50] vanishrequires 3 currents, I₁, I₂ and I₃ together with aI₁ =-cI₃ giving thesame condition as above, Eq. [65]. In a practical arrangement we do ofcourse require supports. In the case that some material is left assupport segments at 3 or 4 places around the slot, Eq. [65] will to someextent be violated.

Acoustically controlled and magnetically screened gradient coils

So far we have been mainly concerned with the design of gradient coilswhich are acoustically controlled but which do not have inherent activemagnetic screening present. In the Section on Magnetic Screening withActive Acoustic Control we mentioned briefly the possibility of addingactive magnetic screening to extant gradient coils designed primarily toreduce acoustic noise. The difficulty with this approach is thataddition of a magnetic screen around such a coil assembly would itselfrequire an acoustic force shield so that potential noise generated by itcould also be attenuated. In addition, more space or a greater radialbuild would be required to accommodate the additional features of thegradient coil system. In this Section, therefore, we return to thequestion of combining from the outset active magnetic screening withactive acoustic control.

For our purposes we now consider the design of standard magneticallyscreened fingerprint type cylindrical gradient coil systems. We pose thequestion; can we include in the basic gradient coil design a means toreduce the acoustic noise without impairing or in any way compromisingthe magnetic screening properties of the coil? The standard design ofmagnetically screened coils requires essentially two cylindrical coils;a primary 171 on a cylinder of radius a and a magnetic screen 172 woundon a cylinder of radius c coaxial with the primary coil. Thisarrangement is sketched in FIG. 17a. In this figure we also interpose anacoustic shield 173,174 arrangement with wires at radii b,b' which liessomewhere between a and c, a distance x₁ from the primary. The distancebetween the primary coil and magnetic screen is x. In this newarrangement we shall assume that the space between the primary andmagnetic screen is filled with two different materials forming twoseparate cylindrical annuli of thicknesses x₁ and x₂ with acousticpropagation velocities v₁ and v₂ and attenuations α₁ and α₂respectively. We are now in a position to apply the cylindrical wavetheory developed hereinbefore.

To find the optimum position for an acoustic screen we require that thephase and amplitude of the wave emitted from the surface of radius a andarriving at the surface of radius b is equal and opposite to thecylindrical wave emitted at the surface of radius c arriving at thesurface of radius b'. From our previous analysis we canstraightforwardly write down the condition when b≈b' as ##EQU27## whereI₁ and I₃ are the currents in the primary coil and magnetic screeningcoil. Strictly speaking we should be looking at the force acting on theprimary and magnetic screen surfaces. As an example we consider az-gradient coil comprising a set of cylindrical hoops the relationshipbetween these two currents is given by ##EQU28## where n_(a) and n_(c)are the numbers of turns on the primary coil and magnetic screenrespectively. For n_(a) =n_(b), Eq. [67] can be substituted in Eq. [66]to give ##EQU29##

The conditions for equalisation of Eq. [68] are: for phase;

    k.sub.1 x.sub.1 =k.sub.2 x.sub.2                           [ 69]

for geometrical constraint;

    x.sub.1 +x.sub.2 =c-a=Δ                              [70]

and finally for modulus of amplitude ##EQU30##

In order to obtain an overall simultaneous solution of the above threeequations, we solve Eq. [69] and Eq. [70] simultaneously knowing k₁ andk₂. This fixes x₁ and x₂. These values are then substituted into Eq.[71] together with known values of α₁ and α₂ which allow Eq. [71] to besolved producing a value of the primary radius a necessary to supportthe simultaneous solution of Eq. [68]. An alternative approach is tochoose the ratio a/c and solve Eq. [71] approximately by ignoring theattenuation terms to give k₁ /k₂. Using this ratio x₁ and x₂ can befound allowing an iteration of k₁ /k₂ and x₁ and x₂.

Of course it may be that the velocities and attenuations available incertain materials will not permit a solution with a required value of a.With common materials there is, in fact, a considerable choice ofpropagation velocity to choose from. In general our experience is thatfor materials with high propagation velocity the attenuation per unitlength is often smaller than in materials with a lower propagationvelocity. For fine adjustment in the solution of the equations andespecially if a specific value of primary radius a is required, the twoannuli of thickness x₁ and x₂ may themselves comprise a compositestructure made of concentric cylinders, the material and thickness beingchosen to produce the required average velocity and requiredattenuation. Alternatively filler materials may be added to the plasticsin order to change their intrinsic wave velocities to those required.For example, addition of glass beads or fibres will increase thevelocity as will addition of alumina crystals. FIG. 17b is a sketch of atransverse fingerprint type magnetically screened gradient coil 171 (notshown) mounted on the inner surface with screen 172. Also shown is one176 surface forming part of the acoustic shield. The coils on each ofthe two cylinders 177,178 are potted in two different materials.

What is important is the simple fact that such a solution to theacoustic problem is in principle possible and that with such a solutionno additional price is paid in terms of loss of magnetic screening orloss or change of magnetic field strength at the centre of the coilsystem. The latter is because the acoustic screen comprises two coilstructures and a current distribution which produces zero magnetic fieldat the centre of the coil system. Between the two coil structures wouldbe a very thin air space or soft support for the inner and outercylinders.

The wire pattern for the two coils comprising the acoustic screen areessentially the same if b≃b'. The pattern detail per quadrant fortransverse fingerprint coils is largely arbitrary and could be aradially registered version of either the inner or primary magnetic coilof radius a or the outer magnetic screen coil at radius c. If b≠b' wecan even look for suitable solutions when the half acoustic screen atradius b is radially registered with the primary coil and the secondhalf of the acoustic screen at radius b' is radially registered with theouter magnetic screen. Whichever route is chosen, the azimuthal symmetrymust follow the gradient coil symmetry in order to prevent excitation ofcylindrical flexing modes distorting the supporting annuli from circularto elliptic form. We also assume no wave propagation along the z-axissince we have set m=0. See later subsection Acoustic Control withMagnetic Screening.

Experimental results

In this section we present experimental results for a rectangular coilwith re-entrant loop and a closed arc loop segment with re-entrant loop.A sketch showing the experimental arrangement and dimensions for bothloop arrangements is shown in FIG. 12. Using the experimentalarrangement shown earlier in FIG. 5 we have measured the acousticresponse of a rectangular coil. Typical results are plotted in FIG. 18.The squares show the acoustic response when the inner and outer loopscarry the same current in anti-phase. The circles show the acousticresponse when the phase only is optimised to reduce acoustic output.When phase and amplitude of the inner loop or the outer loop is changedto minimise the acoustic output, the results shown as triangles areobtained. The superscripts 1 and 2 mean that current 1 is held constantand current 2 varied to obtain a minimum or current 2 is held constantand current 1 is varied to obtain a minimum acoustic output. In bothcases an iterative procedure is used to provide the best combination ofphase φ and current ratio. The continuous line is the theoreticalexpression, Eq. [31] for θ=α=0. It is noted that in the optimumsituation noise output attenuation of 40-50 dB is straightforwardlyobtained.

The residual noise output level is thought to arise from the currentdrive circuit and the coupling from the drive to the coil support board.The general behaviour of the rectangular loop is well described by Eqs.[14 and 31]. FIG. 19 shows a graph of phase angle φ versus frequency ffor the data shown in FIG. 18. It is clear that phase does notnecessarily follow a single curve but can hop from one curve to anotheras predicted. From the dimensions of the board, the data of FIG. 18 andEq. [3], we deduce that τ=111.11 μs giving a propagation velocity v=0.9kms⁻¹. The board material was unfilled solid polystyrene and the boardthickness was 12 mm. Both the inner and outer wire loops comprise threeturns of 16 s.w.g (1.6 mm) copper wire. The receiving microphone wasapproximately 1 m from the board which was placed within a magnet suchthat its plane was orthogonal to the magnet axis and therefore fielddirection. The best results obtained were for an unfilled central slotforming an air gap, although other arrangements were tried in which theslot was filled with either glass filled epoxy or rubber.

Similar experiments were performed on closed arc loop segments mountedon solid polystyrene (a) and Perspex (b) with re-entrant coils. In thesearrangements the central slots were left unfilled. FIG. 20 shows themeasured acoustic responses and FIG. 21 the corresponding phasevariations. From the dimensions of the arc segments, the data of FIG. 20and Eq. [3], we deduce that for both materials and within experimentalerror τ=83.33 μs giving a common propagation velocity v=0.84 kms⁻¹.

Relatively little data were obtained on this arrangement but what thereis confirms that deforming a rectangular structure into a closed arcloop segment does not vitiate the principle of acoustic control andconfirms our theoretical results, Eqs. [50 and 61], that almost completenullification of acoustic output in such arc segments is possible. Thephase data also confirm the general behaviour predicted by Eq. [51]. Aswith the rectangular coil results, the coils in both the outer loop andthe inner re-entrant loop were given three turns of 16 s.w.g. copperwire.

These results substantiate the theory developed so far but it isemphasised that they have been obtained on isolated flat coils whichwould form the basis of a building block to create a transverse gradientcoil arrangement. It remains to be seen experimentally whether a fullblown gradient set would have the same degree of acoustic outputattenuation as is achieved in an isolated coil section.

Acoustic control with magnetic screening

We have considered above the case when an acoustic shield comprisingcylindrical coils with radii b, b' is inserted into a standardmagnetically screened gradient coil. In that treatment two factors havebeen ignored, namely (i) we have neglected the residual magnetic fieldgradient generated by the field at the coil centre and (ii) we have usedan arbitrary wire pattern for each half of the acoustic screen. We nowaddress these two points by considering the mathematical treatment for afully screened, fully force shielded cylindrical gradient set in whichboth the primary coil and magnetic screen, with radii a, b respectively,are matched with additional cylindrical coils of radii f, F forming theacoustic shield. However, before describing this we briefly recapitulateon the Fourier space design method (R. Turner and R. Bowley. Passivescreening of switched magnetic field gradients J. Phys. E. 19, 876-879(1986). (R. Turner. A target field approach to optimal coil design J.Phys. D: Appl. Phys. 19, L147-L151 (1986) (P. Mansfield and B. Chapman.Multi-shield active magnetic screening of gradient coils in NMR. J. Mag.Res. 72, 211-223 (1987)) for cylindrical distributed wire coils.

Let the x-gradient primary coil of cylinder radius a be characterised bythe surface current stream function S_(a) (ψ,Z). Wirepaths are given bycontours of S_(a). The current distribution is described by

    J=-∇S.sub.a ×n                              [72]

where n is the unit vector normal to the cylinder surface at any point.J has the following components: ##EQU31##

The mth component in the Fourier transform of Eq. [74] is

    J.sub.ψ.sup.m (k)=ik S.sub.a.sup.m (k)                 [75]

where ##EQU32## and

    S.sub.a.sup.m (k)=FT{S.sub.a (ψ,z)}.                   [77]

We emphasise that the symbol k used here and below now signifiesreciprocal space in the magnetic design process. From now on theacoustic wave propagation constant is denoted by q.

For an x-gradient coil only S_(a) ¹ and S_(a) ⁻¹ are non-zero.

The internal field is given by ##EQU33##

The external field is given by ##EQU34## where r is the radial polarco-ordinate. Active Acoustic shields

We now add a second coil to form an acoustic shield which is alsocharacterised by a surface current stream function S_(f) (ψ,z) which issimilar to that being shielded, which resides on a cylinder of radius f.For acoustic control we require that ##EQU35##

This ensures that the wirepaths are radially registered, that is to say,they have the same values of z,ψ on each coil and the correct ratio ofcurrents given by 1:aA/f.

Acoustic Shielding and Active Magnetic Screening

We now consider four coils wound on cylindrical surfaces, the primaryand magnetic screen on radii a and b respectively, and the primaryacoustic shield and the magnetic screen acoustic shield on radii f,Frespectively. See FIG. 22 for general coil assembly layout. The relevantstream functions for this arrangement are tabulated below.

    ______________________________________                                        radius  Stream Function                                                                              Function                                               ______________________________________                                        a       S.sub.a        primary coil                                           f       S.sub.f        acoustic shield for primary                            b       S.sub.b        active magnetic screen                                 F       S.sub.F        acoustic shield for magnetic                                                  screen                                                 ______________________________________                                    

For acoustic control we require that ##EQU36## and also that ##EQU37##thereby producing two radially registered pairs of coils. The constantsA,B are dependant on the acoustic properties of the support media.Because of current phase shifts introduced into the acoustic shield, wecannot produce total field cancellation for r>b. We therefore restrictthis condition to fields from the primary coil and magnetic screen only.For field cancellation at radii r>b we need

    a I.sub.1 '(ka)S.sub.a.sup.1 (k)+bI.sub.1 '(kb)S.sub.b.sup.1 (k)=0.[83]

The internal field of the acoustic shield only at radii r<a iscontrolled by the kernel

    T.sub.i =fK.sub.1 '(kf)S.sub.f.sup.1 (k)+FK.sub.1 '(kF)S.sub.F.sup.1 (k).[84]

Rearranging Eq. [12] we get ##EQU38##

The internal field excluding the acoustic shield is given by ##EQU39##where the internal kernel is ##EQU40## and where l=a,b. Using Eqs. [81]and [82] we obtain

    T.sub.i =a S.sub.a.sup.1 (k)K.sub.1 '(ka)+b S.sub.b.sup.1 (k)K.sub.1 '(kb).[88]

Using Eqs. [84] and [85] gives

    T.sub.i =S.sub.a.sup.1 (k)T.sub.i '                        [89]

where the sub-kernel T_(i) ' is ##EQU41##

The target field approach (10) may now be used in which we specifyspatially a field B_(z) (c,ψ,z) within a cylindrical region of radius c.Fourier transforming then gives B_(z) ¹ (c,k) at radius c. Equating theintegrand of Eq. [46] to B_(z) ¹ (c,k) and inverting we obtain for S_(a)¹ (k) the expression ##EQU42##

From our earlier work the constants A and B above are ##EQU43## where,introducing the angular frequency ω, we denote the wave propagationconstants, q₁ =ω/v₁ and q₂ =ω/v₂ for the two media to distinguish from khere used to note reciprocal space in the magnetic design procedure.From Eqs. [81,82] and [84] we obtain the internal sub-kernel for theacoustic shield ##EQU44##

This equation must be minimised for particular values of a,b byinitially ignoring wave attenuation and phase and by varying theindependent variables f,F,v₁ and v₂. The phase and geometricalconstraints, Eqs. [69 and 70] are taken into account later in aniteration process which includes the wave attenuation terms.

In summary, the procedure is therefore to specify B_(z) (c,ψ,z), use Eq.[91] to calculate S_(a) ¹ (k), then use Eq. [85] to calculate S_(b) ¹(k). The minimum internal field for the acoustic screen is determined byEq. [94].

From Eqs. [81] and [82], currents in the acoustic shields are alwaysless than those in the adjacent acoustically shielded coil. Because theacoustic screen is driven from its own generator source at theappropriate amplitude and phase angle, there is no problem with currentbalance. For magnetic screening, Eq. [85] specifies a current ratiobetween the primary and magnetic screen. As in normal non-acousticallyshielded coils, Eq. [85] can be satisfied by varying the ratio ofprimary/screen turns. The same procedure will apply to the acousticshield.

While we have ensured that the screen gives a minimal magnetic fieldcontribution to the required gradient, it is emphasised that there willalso be a small magnetic field generated by the screens outside themagnetic screen, ie for r>b. This is given by ##EQU45## where

    T.sub.o =S.sub.a.sup.1 (k)T.sub.o '                        [96]

and where T₀ ' is given by ##EQU46##

The external field is expected to be relatively small. We conclude,therefore, that acoustic control designs which employ radialregistration of both halves of the acoustic shield with thecorresponding adjacent primary coil and magnetic screen will always giveunwanted magnetic field components at the gradient coil centre as wellas vitiating the magnetic field screening efficacy.

It may be argued that it is more important to preserve the purity of themagnetic gradient by making the acoustic shield magnetic contributionzero at the coil centre. This may be done by setting T_(i) =0 in Eq.[94]. We can also force at least one of the shield coils to be radiallyregistered with the gradient coil. Let coils at radii a and f beradially registered. Then Eq. [84] may be written as ##EQU47##

The external field from the acoustic shield is controlled by the kernelT_(o) given by

    T.sub.o =-aAI.sub.1 '(kf)S.sub.a.sup.1 (k)+FI.sub.1 '(kF)S.sub.F.sup.1 (k).[99]

Substituting for S_(f) '(k) from Eq. [98] we obtain finally for thesub-kernel T_(o) ' ##EQU48##

We see from Eq. [100] that T_(o) '→0 as f→F. Thus for two closely spacedacoustic shield coils as described above, the magnetic screening of thecoil system would not be perfect but could well be acceptable. Thisapproach also allows some flexibility in choosing f and F, therebymaking acoustic matching easier to achieve.

I claim:
 1. An active acoustically controlled magnetic coil system whichis adapted to be placed in a static magnetic field, the coil comprisinga plurality of first electrical conductors and a plurality of at leastsecond electrical conductors, the first and at least the secondconductors being mechanically coupled by means of at least one block ofmaterial with a predetermined acoustic transmission characteristic andin which the first and at least the second conductors are spaced at apredetermined distance apart, first electrical current supply means forsupplying a first alternating current to said plurality of firstelectrical conductors, at least a second electrical current supply meansfor supplying at least a second alternating current to said plurality ofat least second electrical conductors, said first and at least secondcurrents characterized in that they have different and variableamplitudes and different and variable relative phases, both thesefeatures being determined by the acoustic characteristics of thematerial and by its geometry and the predetermined distance, theamplitudes and relative phases of said first and second currents in saidfirst and second conducts being selected specifically to create adestructive interference so as to substantially attenuate acoustic noiseoutput from the coil system.
 2. An active acoustically controlledmagnetic coil system as claimed in claim 1, in which the first andsecond electrical current supply means comprises means for supplyingcurrent waveforms with controllable shape said waveforms being shaped tofit the wave propagation properties characteristics of the mechanicalcoupling material.
 3. An active acoustically controlled magnetic coilsystem as claimed in claim 2, including means for adjusting theamplitude of the second current to be a defined ratio of the amplitudeof the first current, the defined ratio being a function of both thedistance by which the first and second conductors are separated and theacoustic transmission characteristics of the coupling material.
 4. Anactive acoustically controlled magnetic coil system as claimed in claim1 in which the first electrical conductor forms an outer loop and thesecond electrical conductor forms an inner re-entrant loop.
 5. An activeacoustically controlled magnetic coil system as claimed in claim 4 inwhich the coil is a gradient coil and in which the planes in which thecoils are positioned are at a distance z from a datum so as to optimizethe gradient field.
 6. An active acoustically controlled magnetic coilsystem as claimed in claim 4, in which the inner re-entrant loopcomprises first and second substantially parallel path portionsconnected by a relatively short joining portion, the first and secondportions being embedded in first and second separate material blocks,the blocks being mechanically coupled together.
 7. An activeacoustically controlled magnetic coil system as claimed in claim 6, inwhich the mechanical coupling comprises a suitable coupling material. 8.An active acoustically controlled magnetic coil system as claimed inclaim 7, in which the coupling material is a solid polymer materialwhich is different material to that used to support the first conductoror outer loop.
 9. An active acoustically controlled magnetic coil systemas claimed in claim 7, in which the mechanical coupling comprises an airgap with spacers positioned at intervals to separate the first andsecond blocks.
 10. A method of designing an active acousticallycontrolled magnetic coil system comprising the steps of:defining firstand second substantially parallel conductor paths; defining an acoustictransmission material having predetermined characteristics to encase thefirst and second parallel conductors at a predetermined distance apart;determining a first alternating current at a first amplitude and phaseto flow in the first parallel conductor path; determining a secondalternating current at a second variable amplitude and variable relativephase different to said first amplitude and phase to flow in the secondparallel conductor path, the amplitude and relative phase of the secondcurrent being determined by the acoustic characteristics of the materialand by its geometry and the predetermined distance, the amplitudes andrelative phases of said first and second currents in said first andsecond parallel conductors being selected specifically to create adestructive interference so as to substantially attenuate acoustic noiseoutput from the coil system.
 11. A method as claimed in claim 10 inwhich the substantially parallel paths are arcuate when the rectangularloops are deformed into closed arc loops.
 12. An active acousticallycontrolled magnetic coil system including a coil structure comprisingfour substantially parallel conductors in a mechanically coupled systemincluding first and second outer conductors and first and second innerconductors, each first and second outer conductor being mechanicallycoupled to a respective first and second inner conductor by first andsecond blocks of material with defined acoustic transmissioncharacteristics and in which the first and second blocks are connectedtogether by a third acoustically transmissive material and includingfirst and second electrical current supply means for respectivelysupplying first and second currents to said first and second outerconductors and to said first and second inner conductors, said firstcurrent and said second currents being characterized in that they havedifferent and variable amplitudes and different and variable relativephases, both these features being determined by the acousticcharacteristics of the acoustic materials and by the geometries andpredetermined distances, the amplitude and phases of said first andsecond currents in said first and second outer conductors and said firstand second inner conductors being selected specifically to create adestructive interference so as to substantially attenuate acoustic noiseoutput from the coil system.
 13. An active acoustically controlledmagnetic coil system as claimed in claim 12 in which the coil systemfurther comprises magnetic screening coil means.
 14. An activeacoustically controlled magnetic coil system as claimed in claim 13 inwhich the magnetic screening coil means is acoustically screened with acoil structure comprising four substantially parallel conductors in amechanically coupled system including first and second outer conductorsand first and second inner conductors, each first and second outerconductor being mechanically coupled to a respective first and secondinner conductor by first and second blocks of material with definedacoustic transmission characteristics and in which the first and secondblocks are connected together by a third acoustically transmissivematerial and including first and second electrical current supply meansfor respectively supplying first and second currents to said first andsecond outer conductors and to said first and second inner conductors,said first current and said second currents being characterized in thatthey have different and variable amplitudes and different and variablerelative phases, both these features being determined by the acousticcharacteristics of the acoustic materials and by the geometries andpredetermined distances, the amplitude and phases of said first andsecond currents in said first and second outer conductors and said firstand second inner conductors being selected specifically to create adestructive interference so as to substantially attenuate acoustic noiseoutput from the coil system.
 15. An active acoustically controlledmagnetic coil system as claimed in claim 12 in which the material of thefirst and second blocks is identical to the material of the thirdacoustically transmissive material.
 16. An active acousticallycontrolled magnetic coil system as claimed in claim 15 in which theconductors are arranged in arcs.
 17. An active acoustically controlledmagnetic coil system as claimed in claim 16, in which the coils form agradient coil system for an MRI apparatus.
 18. An active acousticallycontrolled magnetic coil system as claimed in claim 12 in which thethird acoustically transmissive material is air, the first and secondblocks being mechanically held together only at defined areas.
 19. Anactive acoustically controlled magnetic coil system as claimed in claim12, in which the third acoustically transmissive material comprises acoupling block of acoustically transmissive material.